On stability analysis with the v-gap metric and integral quadratic constraints

Sei Zhen Khong, Michael Cantoni

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This is part of an effort to extend Vinnicombe's v-gap metric based analysis of uncertain feedback interconnections to a linear time-varying setting. The first results involved using integral quadratic constraints (IQCs) to characterise the uncertainty and the existence of v-gap homotopies. Recent work establishes more familiar results in terms of v-gap balls, via the properties of graph symbols and generalised Wiener-Hopf and Hankel operators revealed by the initial work. In this paper, the additional flexibility of IQC based analysis is reconciled with a v-gap ball based stability result. That is to say, we show the latter can be recovered within the original IQC and v-gap homotopy based framework. To this end, path-connectedness of v-gap balls plays a central role. This is established by exploiting a linear fractional characterisation of the v-gap metric and the existence of a certain J-spectral factorisation, which is shown to be the case for finite-dimensional systems with stabilisable and detectable state-space realisation.

Original languageEnglish (US)
Title of host publicationProceedings of the 2011 Australian Control Conference, AUCC 2011
Pages519-524
Number of pages6
StatePublished - Dec 1 2011
Event1st Australian Control Conference, AUCC 2011 - Melbourne, VIC, Australia
Duration: Nov 10 2011Nov 11 2011

Publication series

NameProceedings of the 2011 Australian Control Conference, AUCC 2011

Other

Other1st Australian Control Conference, AUCC 2011
CountryAustralia
CityMelbourne, VIC
Period11/10/1111/11/11

Keywords

  • Feedback
  • integral quadratic constraints
  • linear fractional transformations
  • path-connectedness
  • time-varying systems
  • v-gap metric

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